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Invariance under symmetry is an important problem in machine learning. Our paper looks specifically at equivariant neural networks where transformations of inputs yield homomorphic transformations of outputs. Here, steerable CNNs have…

State-of-the-art semantic segmentation approaches increase the receptive field of their models by using either a downsampling path composed of poolings/strided convolutions or successive dilated convolutions. However, it is not clear which…

Continuous improvement in medical imaging techniques allows the acquisition of higher-resolution images. When these are used in a predictive setting, a greater number of explanatory variables are potentially related to the dependent…

There has been recent interest in extending the ideas of False Discovery Rates (FDR) to variable selection in regression settings. Traditionally the FDR in these settings has been defined in terms of the coefficients of the full regression…

Controlling the False Discovery Rate (FDR) in a variable selection procedure is critical for reproducible discoveries, and it has been extensively studied in sparse linear models. However, it remains largely open in scenarios where the…

Identifying low-dimensional sufficient structures in nonlinear sufficient dimension reduction (SDR) has long been a fundamental yet challenging problem. Most existing methods lack theoretical guarantees of exhaustiveness in identifying…

Conventional matrix completion methods approximate the missing values by assuming the matrix to be low-rank, which leads to a linear approximation of missing values. It has been shown that enhanced performance could be attained by using…

We explore two primary classes of approaches to dimensionality reduction (DR): Independent Dimensionality Reduction (IDR) and Simultaneous Dimensionality Reduction (SDR). In IDR methods, of which Principal Components Analysis is a…

Algorithms that ensure reproducible findings from large-scale, high-dimensional data are pivotal in numerous signal processing applications. In recent years, multivariate false discovery rate (FDR) controlling methods have emerged,…

Rate of change of frequency (RoCoF) and frequency nadir should be considered in real-time frequency-constrained optimal power flow (FCOPF) to ensure frequency stability of the modern power systems. Since calculating the frequency response…

Single index models provide an effective dimension reduction tool in regression, especially for high dimensional data, by projecting a general multivariate predictor onto a direction vector. We propose a novel single-index model for…

The conventional spatial convolution layers in the Convolutional Neural Networks (CNNs) are computationally expensive at the point where the training time could take days unless the number of layers, the number of training images or the…

We revisit the inverse problem of reconstructing a spatially varying diffusion coefficient in stationary elliptic equations from boundary Cauchy data. From a theoretical perspective, we introduce a gradient-weighted modification of the…

Regression with distribution-valued responses and Euclidean predictors has gained increasing scientific relevance. While methodology for univariate distributional data has advanced rapidly in recent years, multivariate distributions, which…

In this paper, we propose a new approach for facial expression recognition using deep covariance descriptors. The solution is based on the idea of encoding local and global Deep Convolutional Neural Network (DCNN) features extracted from…

This paper develops a framework for testing for associations in a possibly high-dimensional linear model where the number of features/variables may far exceed the number of observational units. In this framework, the observations are split…

Recently, Convolutional Neural Networks (CNN) based image super-resolution (SR) have shown significant success in the literature. However, these methods are implemented as single-path stream to enrich feature maps from the input for the…

Data-driven models, such as FourCastNet (FCN), have shown exemplary performance in high-resolution global weather forecasting. This performance, however, is based on supervision on mesh-gridded weather data without the utilization of raw…

We present a new Cascaded Shape Regression (CSR) architecture, namely Dynamic Attention-Controlled CSR (DAC-CSR), for robust facial landmark detection on unconstrained faces. Our DAC-CSR divides facial landmark detection into three cascaded…

We present a comprehensive theoretical framework for calculating the linear and nonlinear optical responses of time-periodic quantum systems. Using density matrix evolution in the Floquet basis and adopting the length gauge, our approach…